Andrew Valentine

Hamilton's principle and normal mode coupling in an aspherical planet with a fluid core

23 May 2018

A new paper by David Al-Attar has just published in Geophysical Journal International. It describes some of our theoretical work on normal mode seismology, addressing a long-standing problem in the field. In principle, normal mode coupling theory allows the exact seismic response of an Earth-like body to be calculated. However, the traditional theoretical development (based on perturbation theory) did not provide a complete treatment of topography on the body’s surface, or on internal discontinuities. This can lead to small, but potentially important, deficencies in calculations.

Over the last few years, David and his graduate student, Ophelia Crawford, have developed the concept of ‘particle relabelling transformations’. These provide a mechanism by which an Earth model can be perturbed, without altering its seismic response. As we show in the new paper, this allows topography to be handled exactly: in effect, one can transform the model with topography into a seismically-equivalent model without topography. Normal mode calculations can then be performed using the topography-free model, for which exact mathematical results exist.